In the present paper, three-dimensional (3D) turbulent flow in the porous media formed by periodic arrays of particles is numerically investigated. 3D Navier–Stokes equations and a standard k-ε turbulence model with enhanced wall function are adopted to model the turbulent flow inside the pores. Both local and macroscopic turbulence characteristics for different particle types (cubic, spherical, and ellipsoidal particles) and array forms [simple cubic (SC) and body center cubic arrays (BCC)] with different pore Reynolds numbers and porosities are carefully examined. It is revealed that, in the structural arrays of particles, the effects of particle shape and array form would be remarkable. With the same Reynolds number and porosity, the magnitudes of turbulence kinetic energy and its dissipation rate for the simple cubic array of spheres (SC-S) would be higher than those for the other arrays. Furthermore, with a nonlinear fitting method, the macroscopic correlations for extra turbulence quantities k and ɛ in the structural arrays for different particle types and array forms are extracted. The forms of present correlations can fit well with those of Nakayama and Kuwahara's correlations [Nakayama and Kuwahara, 1999, “A Macroscopic Turbulence Model for Flow in Porous Media,” ASME J. Fluids Eng., 121(2), pp. 427–433], but some model constants would be lower.

References

References
1.
de Lemos
,
M. S. J.
,
2006
,
Turbulence in Porous Media
,
Elsevier
,
Amsterdam
.
2.
Dybbs
,
A.
, and
Edwards
,
R. V.
,
1984
, “
A New Look at Porous Media Fluid Mechanics—Darcy to Turbulent
,”
Fundamentals of Transport Phenomena in Porous Media
,
J.
Bear
and
M. Y.
Corapcioglu
, Eds.,
Martinus Nijhoff
, The Hague, The Netherlands, pp.
199
254
.
3.
Teruel
,
F. E.
, and
Rizwan
,
U.
,
2009
, “
A New Turbulence Model for Porous Media Flows. Part I: Constitutive Equations and Model Closure
,”
Int. J. Heat Mass Transfer
,
52
(
19–20
), pp.
4264
4272
.10.1016/j.ijheatmasstransfer.2009.04.017
4.
Nakayama
,
A.
, and
Kuwahara
,
F.
,
2008
, “
A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles
,”
ASME J. Fluids Eng.
,
130
(
10
), p.
1012051
.10.1115/1.2969461
5.
Lage
,
J. L.
,
de Lemos
,
M. J. S.
, and
Nield
,
D. A.
,
2002
, “
Modeling Turbulence in Porous Media
,”
Transport Phenomena in Porous Media II
,
D. B.
Ingham
and
I.
Pop
, Eds.,
Elsevier
,
Oxford, UK
, pp.
198
230
.
6.
Antohe
,
B. V.
, and
Lage
,
J. L.
,
1997
, “
A General Two-Equation Macroscopic Turbulence Model for Incompressible Flow in Porous Media
,”
Int. J. Heat Mass Transfer
,
40
(
13
), pp.
3013
3024
.10.1016/S0017-9310(96)00370-5
7.
Getachew
,
D.
,
Minkowycz
,
W. J.
, and
Lage
,
J. L.
,
2000
, “
A Modified Form of the k-ε Model for Turbulent Flows of an Incompressible Fluid in Porous Media
,”
Int. J. Heat Mass Transfer
,
43
(
16
), pp.
2909
2915
.10.1016/S0017-9310(99)00345-2
8.
Takatsu
,
Y.
, and
Masuka
,
T.
,
1998
, “
Turbulent Phenomena in Flow Through Porous Media
,”
J. Porous Media
,
1
(
3
), pp.
243
251
.
9.
Nakayama
,
A.
, and
Kuwahara
,
F.
,
1999
, “
A Macroscopic Turbulence Model for Flow in Porous Media
,”
ASME J. Fluids Eng.
,
121
(
2
), pp.
427
433
.10.1115/1.2822227
10.
Pedras
,
M. H. J.
, and
de Lemos
,
M. J. S.
,
2001
, “
On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods
,”
ASME J. Fluids Eng.
,
123
(
4
), pp.
941
947
.10.1115/1.1413244
11.
Pedras
,
M. H. J.
, and
de Lemos
,
M. S. J.
,
2001
, “
Macroscopic Turbulence Modeling for Incompressible Flow Through Undeformable Porous Media
,”
Int. J. Heat Mass Transfer
,
44
(
6
), pp.
1081
1093
.10.1016/S0017-9310(00)00202-7
12.
Pedras
,
M. H. J.
, and
de Lemos
,
M. J. S.
,
2001
, “
Simulation of Turbulent Flow in Porous Media Using a Spatially Periodic Array and a Low Re Two-Equation Closure
,”
Numer. Heat Transfer, Part A
,
39
(
1
), pp.
35
59
.10.1080/104077801458456
13.
Pedras
,
M. H. J.
, and
de Lemos
,
M. J. S.
,
2003
, “
Computation of Turbulent Flow in Porous Media Using a Low-Reynolds k-ε Model and an Infinite Array of Transversally Displaced Elliptic Rods
,”
Numer. Heat Transfer, Part A
,
43
(
6
), pp.
585
602
.10.1080/10407780307349
14.
Teruel
,
F. E.
, and
Rizwan
,
U.
,
2009
, “
A New Turbulence Model for Porous Media Flows. Part II: Analysis and Validation Using Microscopic Simulations
,”
Int. J. Heat Mass Transfer
,
52
(
21–22
), pp.
5193
5203
.10.1016/j.ijheatmasstransfer.2009.04.023
15.
Teruel
,
F. E.
, and
Rizwan
,
U.
,
2010
, “
Numerical Computation of Macroscopic Turbulence Quantities in Representative Elementary Volumes of the Porous Medium
,”
Int. J. Heat Mass Transfer
,
53
(
23–24
), pp.
5190
5198
.10.1016/j.ijheatmasstransfer.2010.07.041
16.
Guo
,
B. Y.
,
Yu
,
A.
,
Wright
,
B.
, and
Zulli
,
P.
,
2006
, “
Simulation of Turbulent Flow in a Packed Bed
,”
Chem. Eng. Technol.
,
29
(
5
), pp.
596
603
.10.1002/ceat.200500292
17.
Takeda
,
K
.,
1994
, “
Mathematical Modeling of Pulverized Coal Combustion in a Blast Furnace
,” Ph.D. thesis, Imperial College, London.
18.
Kuwahara
,
F.
,
Yamane
,
T.
, and
Nakayama
,
A.
,
2006
, “
Large Eddy Simulation of Turbulent Flow in Porous Media
,”
Int. Commun. Heat Mass Transfer
,
33
(
4
), pp.
411
418
.10.1016/j.icheatmasstransfer.2005.12.011
19.
Yang
,
J.
,
Wang
,
Q. W.
,
Zeng
,
M.
, and
Nakayama
,
A.
,
2010
, “
Computational Study of Forced Convective Heat Transfer in Structured Packed Beds With Spherical or Ellipsoidal Particles
,”
Chem. Eng. Sci.
,
65
(
2
), pp.
726
738
.10.1016/j.ces.2009.09.026
20.
Yang
,
J.
,
Wang
,
J.
,
Bu
,
S. S.
,
Zeng
,
M.
,
Wang
,
Q. W.
, and
Nakayama
,
A.
,
2012
, “
Experimental Analysis of Forced Convective Heat Transfer in Novel Structured Packed Beds of Particles
,”
Chem. Eng. Sci.
,
71
(
26
), pp.
126
137
.10.1016/j.ces.2011.12.005
21.
ANSYS Inc.
,
2009
,
ANSYS Fluent 12.0 Theory Guide
,
Canonsburg, PA
.
22.
Celik
,
I.
, and
Karatekin
,
O.
,
1997
, “
Numerical Experiments on Application of Richardson Extrapolation With Nonuniform Grids
,”
ASME J. Fluids Eng.
,
119
(
3
), pp.
584
590
.10.1115/1.2819284
23.
Kuwahara
,
F.
,
Kameyama
,
Y.
,
Yamashita
,
S.
, and
Nakayama
,
A.
,
1998
, “
Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array
,”
J. Porous Media
,
1
(
1
), pp.
47
55
.
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